With the increasing deployment of artificial intelligence (AI) technologies, the potential of humans working with AI agents has been growing at a great speed. Human-AI teaming is an important paradigm for studying various aspects when humans and AI agents work together. The unique aspect of Human-AI teaming research is the need to jointly study humans and AI agents, demanding multidisciplinary research efforts from machine learning to human-computer interaction, robotics, cognitive science, neuroscience, psychology, social science, and complex systems. However, existing platforms for Human-AI teaming research are limited, often supporting oversimplified scenarios and a single task, or specifically focusing on either human-teaming research or multi-agent AI algorithms. We introduce \textbf{CREW}, a platform to facilitate Human-AI teaming research in real-time decision-making scenarios and engage collaborations from multiple scientific disciplines, with a strong emphasis on human involvement. It includes pre-built tasks for cognitive studies and Human-AI teaming with expandable potentials from our modular design. Following conventional cognitive neuroscience research, CREW also supports multimodal human physiological signal recording for behavior analysis. Moreover, CREW benchmarks real-time human-guided reinforcement learning agents using state-of-the-art algorithms and well-tuned baselines. With CREW, we were able to conduct 50 human subject studies within a week to verify the effectiveness of our benchmark.